Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{n^2 - 5n + 4}{n^2 - 16}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 - 5n + 4}{n^2 - 16} = \dfrac{(n - 1)(n - 4)}{(n + 4)(n - 4)} $ Notice that the term $(n - 4)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n - 4)$ gives: $p = \dfrac{n - 1}{n + 4}$ Since we divided by $(n - 4)$, $n \neq 4$. $p = \dfrac{n - 1}{n + 4}; \space n \neq 4$